# Hilbertian quantum theory as the theory of complementarity

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## Abstract

It is demonstrated that the notion of complementary physical quantities assumes the possibility of performing ideal first-kind measurements of such quantities. This then leads to an axiomatic reconstruction of the Hilbertian quantum theory based on the complementarity principle and on its connection with the measurement theoretical idealization known as the projection postulate. As the notion of complementary physical quantities does not presuppose the notion of probability, the given axiomatic reconstruction reveals complementarity as an essential reason for the irreducibly probabilistic nature of the quantum theory.

## Keywords

Field Theory Elementary Particle Quantum Field Theory Quantum Theory Physical Quantity
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© Plenum Publishing Corporation 1983